Equivalence Classes

May 2010
13
0
Hello, Im having problems with equivalence classes.

The relation R is defined for complex numbers z=x+yi and w=a+bi. zRw if and only if x+b=y+a

I am asked to give the elements of the equivalence class containg

I have wrote, ={xeC:xRi}={xeC:x-i} to begin finding the equivalence classes, but am stuck trying to find the elements
 

Plato

MHF Helper
Aug 2006
22,461
8,632
Is this true \(\displaystyle (0+1\cdot i)\mathcal{R}(1+0\cdot i)?\)
 
May 2010
13
0
No, because you can't relate the real numbers to the imaginery numbers?
 

Plato

MHF Helper
Aug 2006
22,461
8,632
No, because you can't relate the real numbers to the imaginery numbers?
What are imaginary numbers?
Are they ghosts of dearly departed real numbers?
 
May 2010
13
0
What are imaginary numbers?
Are they ghosts of dearly departed real numbers?
The real numbers are a subset of the complex numbers. a+ib is a complex numbers, so imaginary numbers can be added or subtracted to the realnumber to form a complex number.

I know i^2 is -1

So the equivalence class containing i will just be those elements congruent to i? So the elements would be the complex numbers. Or is this chasing the wrong argument?